Abstract

A two-port polarization-independent tunable spectral slicing filter at the 1530nm wavelength regime is presented. The design utilizes an asymmetric interferometer with a sparse index grating along its arms. The sparse grating makes it possible to select equally spaced frequency channels from an incident WDM signal and to place nulls between them to coincide with the signal comb frequency. The number of selected channels and nulls between them depends on the number of coupling regions used in the sparse grating. The free spectral range depends on the spacing between the coupling regions. The Z-transform method is used to synthesize the filter and determine the spectral response. The operation of a device with six coupling regions is demonstrated, and good agreement with theoretical predictions is obtained. A 3dB bandwidth of 1nm and thermal tuning over a range of 13nm are measured.

© 2011 Optical Society of America

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  1. K. Jinguji and M. Oguma, “Optical half-band filters,” J. Lightwave Technol. 18, 252–259 (2000).
    [CrossRef]
  2. M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
    [CrossRef]
  3. C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foyt, L. T. Gomez, and L. L. Buhl, “Wideband arrayed waveguide grating with three low-loss maxima per passband,” IEEE Photon. Technol. Lett. 18, 2308–2310 (2006).
    [CrossRef]
  4. C. R. Doerr, L. W. Stultz, and R. Pafchek, “Compact and low-loss integrated box-like passband multiplexer,” IEEE Photon. Technol. Lett. 15, 918–920 (2003).
    [CrossRef]
  5. H. F. Taylor, “Tunable spectral slicing filters for dense wavelength-division multiplexing,” J. Lightwave Technol. 21, 837–847 (2003).
    [CrossRef]
  6. R. C. Rabelo, O. Eknoyan, and H. F. Taylor, “Tunable spectral slicing filter utilizing sparse grating in Ti:LiNbO3,” Proc. SPIE 7218, 72180F (2009).
    [CrossRef]
  7. Y. Ping, O. Eknoyan, and H. F. Taylor, “Polarization-independent tunable bandpass filter utilizing symmetric branch beam splitters,” Electron. Lett. 40, 960–962 (2004).
    [CrossRef]
  8. Z. Tang, O. Eknoyan, and H. F. Taylor, “Polarisation-independent electro-optically tunable wavelength filter in LiTaO3,” Electron. Lett. 30, 1758–1759 (1994).
    [CrossRef]
  9. P. Tang, O. Eknoyan, and H. F. Taylor, “Rapidly tunable add-drop multiplexer (OADM) using a static-strain-induced grating in LiNbO3,” J. Lightwave Technol. 21, 236–245 (2003).
    [CrossRef]
  10. J. R. Croston, A. D. Carr, N. J. Parsons, S. N. Radcliffe, and L. J. St. Ville, “Lithium niobate electro-optic tunable filter with high sidelobe suppression,” Electron. Lett. 29, 157–159 (1993).
    [CrossRef]
  11. F. Heismann and R. C. Alferness, “Wavelength-tunable electrooptic polarization conversion in birefringent waveguides,” IEEE J. Quantum Electron. 24, 83–93 (1988).
    [CrossRef]
  12. H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE 62, 1044–1060 (1974).
    [CrossRef]
  13. A. Yariv, “Guided wave optics—propagation in optical fibers,” in Quantum Electronics, 3rd ed. (Wiley, 1989), pp. 623–627.
  14. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, 1st ed. (Wiley, 1999).
  15. K. Jinguji and M. Kawashi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
    [CrossRef]
  16. D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
    [CrossRef]
  17. D. A. Smith, A. D’Alessandro, and J. E. Baran, “Source of sidelobe asymmetry in integrated acousto-optic filters,” Appl. Phys. Lett. 62, 814–816 (1993).
    [CrossRef]
  18. G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
    [CrossRef]
  19. Y.-W. Shin, O. Eknoyan, C. K. Madsen, and H. F. Taylor, “Rapidly tunable optical add-drop multiplexer utilizing relaxed beam splitters,” Electron. Lett. 43, 1428–1430 (2007).
    [CrossRef]

2009

R. C. Rabelo, O. Eknoyan, and H. F. Taylor, “Tunable spectral slicing filter utilizing sparse grating in Ti:LiNbO3,” Proc. SPIE 7218, 72180F (2009).
[CrossRef]

2007

Y.-W. Shin, O. Eknoyan, C. K. Madsen, and H. F. Taylor, “Rapidly tunable optical add-drop multiplexer utilizing relaxed beam splitters,” Electron. Lett. 43, 1428–1430 (2007).
[CrossRef]

2006

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foyt, L. T. Gomez, and L. L. Buhl, “Wideband arrayed waveguide grating with three low-loss maxima per passband,” IEEE Photon. Technol. Lett. 18, 2308–2310 (2006).
[CrossRef]

2004

Y. Ping, O. Eknoyan, and H. F. Taylor, “Polarization-independent tunable bandpass filter utilizing symmetric branch beam splitters,” Electron. Lett. 40, 960–962 (2004).
[CrossRef]

2003

2002

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

2000

1995

K. Jinguji and M. Kawashi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[CrossRef]

1994

Z. Tang, O. Eknoyan, and H. F. Taylor, “Polarisation-independent electro-optically tunable wavelength filter in LiTaO3,” Electron. Lett. 30, 1758–1759 (1994).
[CrossRef]

1993

J. R. Croston, A. D. Carr, N. J. Parsons, S. N. Radcliffe, and L. J. St. Ville, “Lithium niobate electro-optic tunable filter with high sidelobe suppression,” Electron. Lett. 29, 157–159 (1993).
[CrossRef]

D. A. Smith, A. D’Alessandro, and J. E. Baran, “Source of sidelobe asymmetry in integrated acousto-optic filters,” Appl. Phys. Lett. 62, 814–816 (1993).
[CrossRef]

1988

F. Heismann and R. C. Alferness, “Wavelength-tunable electrooptic polarization conversion in birefringent waveguides,” IEEE J. Quantum Electron. 24, 83–93 (1988).
[CrossRef]

1974

H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE 62, 1044–1060 (1974).
[CrossRef]

D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

1967

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

Alferness, R. C.

F. Heismann and R. C. Alferness, “Wavelength-tunable electrooptic polarization conversion in birefringent waveguides,” IEEE J. Quantum Electron. 24, 83–93 (1988).
[CrossRef]

Baran, J. E.

D. A. Smith, A. D’Alessandro, and J. E. Baran, “Source of sidelobe asymmetry in integrated acousto-optic filters,” Appl. Phys. Lett. 62, 814–816 (1993).
[CrossRef]

Bond, W. L.

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

Boyd, G. D.

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

Buhl, L. L.

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foyt, L. T. Gomez, and L. L. Buhl, “Wideband arrayed waveguide grating with three low-loss maxima per passband,” IEEE Photon. Technol. Lett. 18, 2308–2310 (2006).
[CrossRef]

Cappuzzo, M. A.

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foyt, L. T. Gomez, and L. L. Buhl, “Wideband arrayed waveguide grating with three low-loss maxima per passband,” IEEE Photon. Technol. Lett. 18, 2308–2310 (2006).
[CrossRef]

Carr, A. D.

J. R. Croston, A. D. Carr, N. J. Parsons, S. N. Radcliffe, and L. J. St. Ville, “Lithium niobate electro-optic tunable filter with high sidelobe suppression,” Electron. Lett. 29, 157–159 (1993).
[CrossRef]

Carter, H. L.

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

Chen, E. Y.

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foyt, L. T. Gomez, and L. L. Buhl, “Wideband arrayed waveguide grating with three low-loss maxima per passband,” IEEE Photon. Technol. Lett. 18, 2308–2310 (2006).
[CrossRef]

Croston, J. R.

J. R. Croston, A. D. Carr, N. J. Parsons, S. N. Radcliffe, and L. J. St. Ville, “Lithium niobate electro-optic tunable filter with high sidelobe suppression,” Electron. Lett. 29, 157–159 (1993).
[CrossRef]

D’Alessandro, A.

D. A. Smith, A. D’Alessandro, and J. E. Baran, “Source of sidelobe asymmetry in integrated acousto-optic filters,” Appl. Phys. Lett. 62, 814–816 (1993).
[CrossRef]

Doerr, C. R.

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foyt, L. T. Gomez, and L. L. Buhl, “Wideband arrayed waveguide grating with three low-loss maxima per passband,” IEEE Photon. Technol. Lett. 18, 2308–2310 (2006).
[CrossRef]

C. R. Doerr, L. W. Stultz, and R. Pafchek, “Compact and low-loss integrated box-like passband multiplexer,” IEEE Photon. Technol. Lett. 15, 918–920 (2003).
[CrossRef]

Eknoyan, O.

R. C. Rabelo, O. Eknoyan, and H. F. Taylor, “Tunable spectral slicing filter utilizing sparse grating in Ti:LiNbO3,” Proc. SPIE 7218, 72180F (2009).
[CrossRef]

Y.-W. Shin, O. Eknoyan, C. K. Madsen, and H. F. Taylor, “Rapidly tunable optical add-drop multiplexer utilizing relaxed beam splitters,” Electron. Lett. 43, 1428–1430 (2007).
[CrossRef]

Y. Ping, O. Eknoyan, and H. F. Taylor, “Polarization-independent tunable bandpass filter utilizing symmetric branch beam splitters,” Electron. Lett. 40, 960–962 (2004).
[CrossRef]

P. Tang, O. Eknoyan, and H. F. Taylor, “Rapidly tunable add-drop multiplexer (OADM) using a static-strain-induced grating in LiNbO3,” J. Lightwave Technol. 21, 236–245 (2003).
[CrossRef]

Z. Tang, O. Eknoyan, and H. F. Taylor, “Polarisation-independent electro-optically tunable wavelength filter in LiTaO3,” Electron. Lett. 30, 1758–1759 (1994).
[CrossRef]

Gomez, L. T.

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foyt, L. T. Gomez, and L. L. Buhl, “Wideband arrayed waveguide grating with three low-loss maxima per passband,” IEEE Photon. Technol. Lett. 18, 2308–2310 (2006).
[CrossRef]

Heismann, F.

F. Heismann and R. C. Alferness, “Wavelength-tunable electrooptic polarization conversion in birefringent waveguides,” IEEE J. Quantum Electron. 24, 83–93 (1988).
[CrossRef]

Hibino, Y.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

Himeno, A.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

Jinguji, K.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

K. Jinguji and M. Oguma, “Optical half-band filters,” J. Lightwave Technol. 18, 252–259 (2000).
[CrossRef]

K. Jinguji and M. Kawashi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[CrossRef]

Kawashi, M.

K. Jinguji and M. Kawashi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[CrossRef]

Kitoh, T.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

Madsen, C. K.

Y.-W. Shin, O. Eknoyan, C. K. Madsen, and H. F. Taylor, “Rapidly tunable optical add-drop multiplexer utilizing relaxed beam splitters,” Electron. Lett. 43, 1428–1430 (2007).
[CrossRef]

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, 1st ed. (Wiley, 1999).

Mikulyak, R. M.

D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Nelson, D. F.

D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Oguma, M.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

K. Jinguji and M. Oguma, “Optical half-band filters,” J. Lightwave Technol. 18, 252–259 (2000).
[CrossRef]

Pafchek, R.

C. R. Doerr, L. W. Stultz, and R. Pafchek, “Compact and low-loss integrated box-like passband multiplexer,” IEEE Photon. Technol. Lett. 15, 918–920 (2003).
[CrossRef]

Parsons, N. J.

J. R. Croston, A. D. Carr, N. J. Parsons, S. N. Radcliffe, and L. J. St. Ville, “Lithium niobate electro-optic tunable filter with high sidelobe suppression,” Electron. Lett. 29, 157–159 (1993).
[CrossRef]

Ping, Y.

Y. Ping, O. Eknoyan, and H. F. Taylor, “Polarization-independent tunable bandpass filter utilizing symmetric branch beam splitters,” Electron. Lett. 40, 960–962 (2004).
[CrossRef]

Rabelo, R. C.

R. C. Rabelo, O. Eknoyan, and H. F. Taylor, “Tunable spectral slicing filter utilizing sparse grating in Ti:LiNbO3,” Proc. SPIE 7218, 72180F (2009).
[CrossRef]

Radcliffe, S. N.

J. R. Croston, A. D. Carr, N. J. Parsons, S. N. Radcliffe, and L. J. St. Ville, “Lithium niobate electro-optic tunable filter with high sidelobe suppression,” Electron. Lett. 29, 157–159 (1993).
[CrossRef]

Shibata, T.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

Shin, Y.-W.

Y.-W. Shin, O. Eknoyan, C. K. Madsen, and H. F. Taylor, “Rapidly tunable optical add-drop multiplexer utilizing relaxed beam splitters,” Electron. Lett. 43, 1428–1430 (2007).
[CrossRef]

Smith, D. A.

D. A. Smith, A. D’Alessandro, and J. E. Baran, “Source of sidelobe asymmetry in integrated acousto-optic filters,” Appl. Phys. Lett. 62, 814–816 (1993).
[CrossRef]

St. Ville, L. J.

J. R. Croston, A. D. Carr, N. J. Parsons, S. N. Radcliffe, and L. J. St. Ville, “Lithium niobate electro-optic tunable filter with high sidelobe suppression,” Electron. Lett. 29, 157–159 (1993).
[CrossRef]

Stultz, L. W.

C. R. Doerr, L. W. Stultz, and R. Pafchek, “Compact and low-loss integrated box-like passband multiplexer,” IEEE Photon. Technol. Lett. 15, 918–920 (2003).
[CrossRef]

Tang, P.

Tang, Z.

Z. Tang, O. Eknoyan, and H. F. Taylor, “Polarisation-independent electro-optically tunable wavelength filter in LiTaO3,” Electron. Lett. 30, 1758–1759 (1994).
[CrossRef]

Taylor, H. F.

R. C. Rabelo, O. Eknoyan, and H. F. Taylor, “Tunable spectral slicing filter utilizing sparse grating in Ti:LiNbO3,” Proc. SPIE 7218, 72180F (2009).
[CrossRef]

Y.-W. Shin, O. Eknoyan, C. K. Madsen, and H. F. Taylor, “Rapidly tunable optical add-drop multiplexer utilizing relaxed beam splitters,” Electron. Lett. 43, 1428–1430 (2007).
[CrossRef]

Y. Ping, O. Eknoyan, and H. F. Taylor, “Polarization-independent tunable bandpass filter utilizing symmetric branch beam splitters,” Electron. Lett. 40, 960–962 (2004).
[CrossRef]

P. Tang, O. Eknoyan, and H. F. Taylor, “Rapidly tunable add-drop multiplexer (OADM) using a static-strain-induced grating in LiNbO3,” J. Lightwave Technol. 21, 236–245 (2003).
[CrossRef]

H. F. Taylor, “Tunable spectral slicing filters for dense wavelength-division multiplexing,” J. Lightwave Technol. 21, 837–847 (2003).
[CrossRef]

Z. Tang, O. Eknoyan, and H. F. Taylor, “Polarisation-independent electro-optically tunable wavelength filter in LiTaO3,” Electron. Lett. 30, 1758–1759 (1994).
[CrossRef]

H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE 62, 1044–1060 (1974).
[CrossRef]

Wong-Foyt, A.

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foyt, L. T. Gomez, and L. L. Buhl, “Wideband arrayed waveguide grating with three low-loss maxima per passband,” IEEE Photon. Technol. Lett. 18, 2308–2310 (2006).
[CrossRef]

Yariv, A.

H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE 62, 1044–1060 (1974).
[CrossRef]

A. Yariv, “Guided wave optics—propagation in optical fibers,” in Quantum Electronics, 3rd ed. (Wiley, 1989), pp. 623–627.

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, 1st ed. (Wiley, 1999).

Appl. Phys. Lett.

D. A. Smith, A. D’Alessandro, and J. E. Baran, “Source of sidelobe asymmetry in integrated acousto-optic filters,” Appl. Phys. Lett. 62, 814–816 (1993).
[CrossRef]

Electron. Lett.

Y.-W. Shin, O. Eknoyan, C. K. Madsen, and H. F. Taylor, “Rapidly tunable optical add-drop multiplexer utilizing relaxed beam splitters,” Electron. Lett. 43, 1428–1430 (2007).
[CrossRef]

Y. Ping, O. Eknoyan, and H. F. Taylor, “Polarization-independent tunable bandpass filter utilizing symmetric branch beam splitters,” Electron. Lett. 40, 960–962 (2004).
[CrossRef]

Z. Tang, O. Eknoyan, and H. F. Taylor, “Polarisation-independent electro-optically tunable wavelength filter in LiTaO3,” Electron. Lett. 30, 1758–1759 (1994).
[CrossRef]

J. R. Croston, A. D. Carr, N. J. Parsons, S. N. Radcliffe, and L. J. St. Ville, “Lithium niobate electro-optic tunable filter with high sidelobe suppression,” Electron. Lett. 29, 157–159 (1993).
[CrossRef]

IEEE J. Quantum Electron.

F. Heismann and R. C. Alferness, “Wavelength-tunable electrooptic polarization conversion in birefringent waveguides,” IEEE J. Quantum Electron. 24, 83–93 (1988).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foyt, L. T. Gomez, and L. L. Buhl, “Wideband arrayed waveguide grating with three low-loss maxima per passband,” IEEE Photon. Technol. Lett. 18, 2308–2310 (2006).
[CrossRef]

C. R. Doerr, L. W. Stultz, and R. Pafchek, “Compact and low-loss integrated box-like passband multiplexer,” IEEE Photon. Technol. Lett. 15, 918–920 (2003).
[CrossRef]

J. Appl. Phys.

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

J. Lightwave Technol.

Proc. IEEE

H. F. Taylor and A. Yariv, “Guided wave optics,” Proc. IEEE 62, 1044–1060 (1974).
[CrossRef]

Proc. SPIE

R. C. Rabelo, O. Eknoyan, and H. F. Taylor, “Tunable spectral slicing filter utilizing sparse grating in Ti:LiNbO3,” Proc. SPIE 7218, 72180F (2009).
[CrossRef]

Other

A. Yariv, “Guided wave optics—propagation in optical fibers,” in Quantum Electronics, 3rd ed. (Wiley, 1989), pp. 623–627.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, 1st ed. (Wiley, 1999).

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Figures (9)

Fig. 1
Fig. 1

Schematic illustration of the device structure.

Fig. 2
Fig. 2

Sparse grating configuration used for polarization coupling along each arm.

Fig. 3
Fig. 3

Block diagram with Z-transform representation of the interaction region.

Fig. 4
Fig. 4

Five equally spaced zeros (circles) on the unit circle in the z domain.

Fig. 5
Fig. 5

Calculated spectral response for a sparse grating with nulls at 100 GHz spacing using (a) six coupling regions and (b) eight (curves with circles) and ten (curves with triangles) coupling regions. The coupling coefficient used in all cases is 0.15 mm 1 .

Fig. 6
Fig. 6

Transmission spectra for the tested filter with six coupling regions on each arm when input polarization is (a) TM or (b) TE.

Fig. 7
Fig. 7

Normalized transmittance spectra of the tested filter for TM (circles) and TE (diamonds) input polarization; solid curve is the calculated theoretical response.

Fig. 8
Fig. 8

Temperature tuning of the normalized transmission spectrum for TE input polarization at 14 ° C (circles) and 27 ° C (diamonds).

Fig. 9
Fig. 9

Tuning rate of the center peak wavelength with temperature for both TM (circles) and TE (diamonds) polarizations.

Tables (1)

Tables Icon

Table 1 Coupling Strength Values ζ i = κ L i Calculated for a Various Number of Coupling Regions (N)

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

C N = ( i = N 2 M i C M i 1 ϕ ) M 1 C .
M i 1 ϕ = ( e j Δ ϕ 0 0 1 ) ,
Δ = 2 π ν ( n TM n TE ) c ± 2 π Λ ,
Δ p = 2 π | ( n TM n TE ) g ( v p v o ) | c .
M i c = ( a i b i b i * a i * ) ,
a i = e j Δ p L i 2 [ cos δ L i + j ( Δ p / 2 ) δ sin δ L i ] ,
b i = e j Δ p L i 2 [ j κ δ sin δ L i ] ,
M i 1 ϕ ( z ) = ( z 1 0 0 1 ) .
a i = cos κ L i ,
b i = j sin κ L i .
C N ( z ) = ( A ( z ) j B R ( z ) j B ( z ) A R ( z ) ) ,
B ( z ) = 1 6 ( 1 + z 1 + z 2 + z 3 + z 4 + z 5 ) ,
( E TE E TM ) T = 1 / 2 [ ( E TE E TM ) U + ( E TE E TM ) L ] ,
( E TE E TM ) T = 1 2 M O A ( E TE E TM ) i ,
M O A = ( 0 j [ e j β TE Λ 2 + e j β TM Λ 2 ] B R ( z ) j [ e j β TM Λ 2 + e j β TE Λ 2 ] B ( z ) 0 ) .
P out = | B ( z ) | 2 2 { 1 cos [ 2 π λ ( n TE n TM ) Λ 2 ] } ( P TE + P TM ) i .
( E TE E TM ) U = 1 / 2 M λ / 4 M Λ / 2 C N ( Z ) M λ / 4 ( E TE E TM ) i .
M λ / 4 = ( e j π / 2 0 0 e j π / 2 ) .
M Λ / 2 = ( e j β TE Λ z 0 0 e j β TM Λ z ) .
( E TE E TM ) L = 1 / 2 C N ( z ) M Λ / 2 ( E TE E TM ) i ,

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